2r^2+6r+1=0

Solution for 2r^2+6r+1=0 equation:

Simplifying
2r2 + 6r + 1 = 0

Reorder the terms:
1 + 6r + 2r2 = 0

Solving
1 + 6r + 2r2 = 0

Solving for variable 'r'.

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
0.5 + 3r + r2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 3r + -0.5 + r2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 3r + r2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 3r + r2 = 0 + -0.5
3r + r2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
3r + r2 = -0.5

The r term is 3r.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3r + 2.25 + r2 = -0.5 + 2.25

Reorder the terms:
2.25 + 3r + r2 = -0.5 + 2.25

Combine like terms: -0.5 + 2.25 = 1.75
2.25 + 3r + r2 = 1.75

Factor a perfect square on the left side:
(r + 1.5)(r + 1.5) = 1.75

Calculate the square root of the right side: 1.322875656

Break this problem into two subproblems by setting 
(r + 1.5) equal to 1.322875656 and -1.322875656.

Subproblem 1
r + 1.5 = 1.322875656

Simplifying
r + 1.5 = 1.322875656

Reorder the terms:
1.5 + r = 1.322875656

Solving
1.5 + r = 1.322875656

Solving for variable 'r'.

Move all terms containing r to the left, all other terms to the right.

Add '-1.5' to each side of the equation.
1.5 + -1.5 + r = 1.322875656 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + r = 1.322875656 + -1.5
r = 1.322875656 + -1.5

Combine like terms: 1.322875656 + -1.5 = -0.177124344
r = -0.177124344

Simplifying
r = -0.177124344

Subproblem 2
r + 1.5 = -1.322875656

Simplifying
r + 1.5 = -1.322875656

Reorder the terms:
1.5 + r = -1.322875656

Solving
1.5 + r = -1.322875656

Solving for variable 'r'.

Move all terms containing r to the left, all other terms to the right.

Add '-1.5' to each side of the equation.
1.5 + -1.5 + r = -1.322875656 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + r = -1.322875656 + -1.5
r = -1.322875656 + -1.5

Combine like terms: -1.322875656 + -1.5 = -2.822875656
r = -2.822875656

Simplifying
r = -2.822875656

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {-0.177124344, -2.822875656}